General Relativity for the Gifted Amateur: errata

When you find errors in the book we would be grateful if they could be emailed to tom.lancaster_at_durham.ac.uk.

Corrections to the second reprinted edition (December 2025)

These errors occur in the first printings and also the first corrected reprint, which can be identified by the noted dated December 2025 at the end of the preface.

Page 283, eq. 27.11 : On the right-hand side, dx² should be dr².
Page 295, sidenote 20: acceleration in cm s^-1 should be cm s^-2.
Page 300, eq. 29.6: On the right-hand side, the term in dr² should read r²/Δ (i.e. the Δ is not squared).
Page 301, eq. 29.9: and also exercise 29.5: g should be g^1/2.
Page 313, example 30.5, final paragraph: the expression in the text should read z = – (a² – x² – y²)^1/2 + a. Then, in the expression z = (1/2a²)(x² + y²), the factor a should not be squared.
Page 318, eqn 30.64: In the third equation, e₁ should read e_θ. In the second and third equations, the factor a should be removed from terms multiplying e_θ and e_φ.
Page 319, eqn 30.69: In the second equation, insert a minus sign before g₂₁/g. In the third equation: the right-hand side should read g₁₁/g.
Page 346, eqn 33.38: The Kronecker delta before the second equals sign should read δ^μ₁.
Page 360, eqn 34.56: t^α should be u^α.
Page 372, eqns 35.47, 35.49, 35.50 and 35.51: the variable s should be λ.
Page 376, Example 36.2, eqns 36.17 to 36.19: remove factors of 1/2 in front of the expressions.
Page 381: sidenote 11: the superscript θ is missing a hat at the end of the penultimate line.
Page 383, eqn 36.81: in the expression for the time components on the left, the part in the brackets should have a single dot, rather than a double dot (i.e. \dot{a}/a); in the expression for the spatial components, the final term (\dot{a}/a) should be squared.
Page 383, sidenote to Example 36.6: In the formula for the timelike basis vector there should not be a minus sign before Φ. In the associated vielbein components for t, replace φ by Φ.
Page 383, eqn 36.85, first line: in the wedge product at the end, θ should be r.
Page 383, eqn 36.85, third line: the expression should read:

Page 396, eqn 37.66: the terms in the square brackets should be swapped.
Page 396, eqn 37.70: remove minus sign from the left-hand side.
Page 589: answer to 4.4(c): “related by a factor r” should read “related by a factor r².
Page 602, eqn E.270, final line: there should be a minus sign in front of the first term on the right-hand side.
Page 603: eqn E.283, final line: g_0α should read g_σα.

Corrections to the first printed edition (2025)

These errors occur in the first printings (Dated Nov 11, 2024 in the preface), but have been corrected in subsequent reprintings, which can be identified by a note added at the end of the preface.

Page 7, eqn 7: missing factor of 3^1/2 on the right hand side.
Page 48, sidenote 9: the position of the subscript ‘0’ and label ‘obs’ should be swapped, such that ‘0’ becomes the superscript.
Page 53, below 4.51: the variable given as rho on the right hand side of the expression, should be a p.
Page 58, sidenote 7: y = r cosθ should read r sinθ.
Page 94: eqn 8.17: the first term on the right-hand side of the second equation is missing a factor cosθ.
Page 98, eq. 8.38 should read dr/dt = [(r – 2GM)/(r + 2GM)]^1/2.
Page 103 , eqn 9.9, 3rd equation: inside the bracket on the right-hand-side, the factor of dr/dλ should be squared.
Page 104, eqn 9.23: the index μ in the variable x^μ on the right-hand-side should be ν.
Page 105: eqn 9.36: the expression for Γ^v_uu should have a in the denominator rather than u.
Page 112, eqn 10.28, line 2: the subscript “r-hat” on the “e” should be “θ-hat”.
Page 123: Example 11.2, second derivative of sⁱ halfway down the final paragraph: delete factor of m on the left-hand side.
Page 127: Two instances of “(3,1)” should be “(1,3)”.
Page 129, eqn 11.38: missing minus sign on right-hand side.
Page 164, sidenote 22: a(t₀) should be squared.
Page 166, eqn 15.32: dt should be squared.
Page 166, penultimate paragraph T^μ should read T^μ^ν.
Page 171, sidenote, line 3: in the penultimate equation for the spatial components of the Ricci tensor, the final term should be 2k/a², rather than 2k/a.
Page 177, caption to Fig 16.6: t_ob+δt_em should read t_ob+δt_ob.
Page 179, exercise 16.4(c): In eq (16.54), R_rr = Λ’/r should be 2Λ’/r. In part (d), the first part of eqn 16.55 should read, Λ’ = Kr exp(2Λ). In the second part, the factor in exp(-Λ) should read exp(-2Λ).
Page 181:2 lines before eqn 17.1: the potential energy should be written V=-GMm/r, rather than U.
Page 182, sidenote: in the penultimate equation for the spatial components of the Ricci tensor, the final term should be 2k/a², rather than 2k/a. This correction is also required in the first line of eqn 17.5.
Page 185, eqn 17.23: insert a factor of 2 in front of ρ_r⁽⁰⁾ .
Page 185, eqn 17.31: the right-hand side should be multiplied by a factor H₀².
Page 186, two lines before eqn 17.30: the expression for ρ_c⁽⁰⁾ should read 3H₀²/8π.
Page 200, eqn 18.50: the equation for T should include the factor (1-x²) rather than (1-x).
Page 205, caption to Fig 19.6: remove prime from r‘ and t‘.
Page 209, line after eqn 19.21: the variable t and r should be primed.
Page 214, eqn 19.37: sin²φ should read sin²χ.
Page 219, sidenote 4, eqn 20.2: In the 4^th term of the right hand side of the first line, the dot should be removed from r (i.e. we do not take the time derivative of this variable in this term).
Page 224, text above eqn 20.36: there should be a factor r₁² in the denominator for K₁.
Page 224, eqn 20.37: the prefactor should be K₁/u₁, rather than u₁/K₁.
Page 226: Caption to Fig 20.8(c): should read n>-1.
Page 233, eqn 21.28: insert minus sign on the right-hand side.
Page 235, eqn 21.39: insert factors of 2 in front of Φ and Λ in the exponentials.
Page 236, exercise 21.8: remove factors of 8π from the given components of T_μν.
Page 239, section 22.2, line 6: insert minus sign on the right-hand side of the in-line equation.
Page 242, sidenote 14: insert a factor 1/r before the components of e_θ and a factor 1/rsinθ before the components of e_φ.
Page 248, eqn 23.5: in the first bracket, r should be r₊.
Page 248, eqn 23.9: on the right-hand side, r₊ should not be squared.
Page 250, sidenote 8: the formula towards the end should read u₀²(1 – ε²) = -2Em/L² (i.e. the square on u₀ is missing).
Page 250, just before eq. 23.21: “we write ε²u₀² = …” (i.e. the ε should be squared).
Page 251, eqn 23.22: the first = sign should be a + sign.
Page 253, eqn 23.32: On the right-hand side, Ẽ should be squared.
Page 254, sidenote 3, line 2: remove square root sign.
Page 257, eqn 24.22: 2cosφ should be cos2φ. Int the text below this, “Total deflection Δφ” should read “deflection δφ”. In equation 24.23, Δφ should then read δφ.
Page 266, eqn 25.10: replace the + sign with a – sign.
Page 268, sidenote 15: insert a – sign on the right-hand side of the first equation.
Page 277, eqn 26.26: the term +2dUdr should read -2dUdr.
Page 278, eqn 26.34: U_r should read u_r.
Page 292, sidenote 12: the reference should be to eqn 28.11, rather than 28.12.
Page 294, sidenote 17, eqn 28.21: replace the two instances of -dW with +dW.
.Page 449, eqn 41.9: in the the first term on the right-hand side, φ should not be squared.
Page 554, eqn A1: all terms on the right-hand side should be squared.
Page 562: sidenote 4: “covariant” should read “contravariant”.
Page 563: “contravariant” should read “covariant”.
Page 584, eqn D.20 and following line: the variable θ should be φ.
Page 588, problem 4.4: in the equation, r = x² + y² + z², the radius r should read r².
Page 589, problem 4.4, in the second of eqns E.23, a factor of r is missing from all three of the terms on the right-hand side.
page 591, eqn E.71: there is an additional nonzero connection coefficient: Γ^r_tt = –Ωr².
Page 595, question 18.6(c): the equation for the hyperbolic curve should read T²–X²=1.
Page 595, question 18.8: the factors (1-x) should read (1-x²).
Page 598, question 23.4, eqn E208: insert a factor of 2 before the middle term in the brackets on the right-hand side.
Page 599, eqn E.214: There should be a factor 1/L̃ before the brackets.
Page 600, question 25.4: In the final paragraph, the two instances of L̃/M=4M, should read L̃/M=4.

With grateful thanks to John Camm, Jay Epstein, Zhanzhi He, Joey LH Ooi, Leslie Rysdale and Congzhou Mike Sha.

Last updated 16/02/26